Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19097698 | C2 | semidirect |
| 3. C2×#19097697 | C2 | semidirect |
| 4. #23757272 | C2 | semidirect |
| 5. #23757142 | C2 | semidirect |
| 6. #23757041 | C2 | semidirect |
| 7. #417×C157 | C2 | semidirect |
| 48. C4×Dic157 | D4 | semidirect |
| 128. C157 | #2039 | semidirect |
| 134. #417 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757851 | 2 |
| C2×#19097698 | 2 |
| C2×#19097697 | 2 |
| #23757272 | 2 |
| #23757142 | 2 |
| #23757041 | 2 |
| #417×C157 | 2 |
| #2039 | 157 |